This force arises as a result of deformation (changes in the initial state of matter). For example, when we stretch a spring, we increase the distance between the molecules of the spring material. When we compress the spring, we decrease it. When we twist or shift. In all these examples, a force arises that prevents deformation - the elastic force.
Hooke's law
The elastic force is directed opposite to the deformation.
Since the body is represented as a material point, the force can be depicted from the center
When connected in series, for example, springs, the stiffness is calculated by the formula
When connected in parallel, the stiffness
Sample stiffness. Young's modulus.
Young's modulus characterizes the elastic properties of a substance. This is a constant value that depends only on the material, its physical state. Characterizes the ability of a material to resist tensile or compressive deformation. The value of Young's modulus is tabular.
Body weight
Body weight is the force with which an object acts on a support. You say it's gravity! The confusion occurs in the following: indeed, often the weight of the body is equal to the force of gravity, but these forces are completely different. Gravity is the force that results from interaction with the Earth. Weight is the result of interaction with the support. The force of gravity is applied at the center of gravity of the object, while the weight is the force that is applied to the support (not to the object)!
There is no formula for determining weight. This force is denoted by the letter .
The support reaction force or elastic force arises in response to the impact of an object on a suspension or support, therefore the body weight is always numerically the same as the elastic force, but has the opposite direction.
The reaction force of the support and the weight are forces of the same nature, according to Newton's 3rd law they are equal and oppositely directed. Weight is a force that acts on a support, not on a body. The force of gravity acts on the body.
Body weight may not be equal to gravity. It can be either more or less, or it can be such that the weight is zero. This state is called weightlessness. Weightlessness is a state when an object does not interact with a support, for example, a state of flight: there is gravity, but the weight is zero!
It is possible to determine the direction of acceleration if we determine where the resultant force is directed.
Note that weight is a force, measured in Newtons. How to correctly answer the question: "How much do you weigh"? We answer 50 kg, naming not weight, but our mass! In this example, our weight is equal to gravity, which is approximately 500N!
Overload- the ratio of weight to gravity
Strength of Archimedes
Force arises as a result of the interaction of a body with a liquid (gas), when it is immersed in a liquid (or gas). This force pushes the body out of the water (gas). Therefore, it is directed vertically upwards (pushes). Determined by the formula:
In the air, we neglect the force of Archimedes.
If the Archimedes force is equal to the force of gravity, the body floats. If the Archimedes force is greater, then it rises to the surface of the liquid, if it is less, it sinks.
electrical forces
There are forces of electrical origin. Occur in the presence of an electric charge. These forces, such as the Coulomb force, the Ampère force, the Lorentz force.
Newton's laws
Newton's I law
There are such systems of reference, which are called inertial, with respect to which the bodies keep their speed unchanged, if they are not affected by other bodies or the action of other forces is compensated.
Newton's II law
The acceleration of a body is directly proportional to the resultant of the forces applied to the body and inversely proportional to its mass:
Newton's third law
The forces with which two bodies act on each other are equal in magnitude and opposite in direction. 
Local frame of reference - this is a frame of reference, which can be considered inertial, but only in an infinitely small neighborhood of any one point of space-time, or only along any one open world line.
Galilean transformations. The principle of relativity in classical mechanics.
Galilean transformations. Consider two frames of reference moving relative to each other and with a constant speed v 0. One of these frames will be denoted by the letter K. We will consider it stationary. Then the second system K will move rectilinearly and uniformly. We choose the coordinate axes x,y,z of the system K and x",y",z" of the system K" so that the x and x" axes coincide, and the y and y" , z and z" axes are parallel to each other. Let's find the relationship between coordinates x,y,z of some point P in system K and coordinates x",y",z" of the same point in system K". "+v 0 , moreover, it is obvious that y=y", z=z". Let us add to these relations the assumption accepted in classical mechanics that time in both systems flows in the same way, that is, t=t". We obtain a set of four equations: x=x"+v 0 t;y=y";z=z"; t=t", called Galilean transformations. Mechanical principle of relativity. The position that all mechanical phenomena in different inertial reference frames proceed in the same way, as a result of which it is impossible to establish by any mechanical experiments whether the system is at rest or moves uniformly and rectilinearly is called the principle of relativity of Galileo. Violation of the classical law of addition of velocities. Based on the general principle of relativity (no physical experience can distinguish one inertial frame from another), formulated by Albert Einstein, Lawrence changed Galileo's transformations and obtained: x "= (x-vt) / (1-v 2 / c 2); y "=y; z "= z; t" \u003d (t-vx / c 2) / (1-v 2 / c 2). These transformations are called Lawrence transformations.
The greater the deformation of the body, the greater the elastic force arises in it. This means that the deformation and the elastic force are interrelated, and a change in one value can be used to judge a change in the other. So, knowing the deformation of the body, it is possible to calculate the elastic force arising in it. Or, knowing the force of elasticity, determine the degree of deformation of the body.
If a different number of weights of the same mass is suspended from a spring, then the more of them are suspended, the more the spring will stretch, that is, it will deform. The more the spring is stretched, the greater the elastic force arises in it. Moreover, experience shows that each subsequent suspended weight increases the length of the spring by the same amount.
So, for example, if the original length of the spring was 5 cm, and hanging one weight on it increased it by 1 cm (i.e., the spring became 6 cm long), then hanging two weights would increase it by 2 cm (total length will be 7 cm ), and three - by 3 cm (the length of the spring will be 8 cm).
Even before the experiment, it is known that the weight and the elastic force arising under its action are directly proportional to each other. A multiple increase in weight will increase the strength of elasticity by the same amount. Experience shows that the deformation also depends on the weight: a multiple increase in weight increases the change in length by the same factor. This means that by eliminating the weight, it is possible to establish a directly proportional relationship between the elastic force and deformation.
If we denote the elongation of the spring as a result of its stretching as x or as ∆l (l 1 - l 0, where l 0 is the initial length, l 1 is the length of the stretched spring), then the dependence of the elastic force on tension can be expressed by the following formula:
F control \u003d kx or F control \u003d k∆l, (∆l \u003d l 1 - l 0 \u003d x)
The formula uses the coefficient k . It shows the exact relationship between the elastic force and elongation. Indeed, elongation for each centimeter can increase the elastic force of one spring by 0.5 N, the second by 1 N, and the third by 2 N. For the first spring, the formula will look like F control \u003d 0.5x, for the second - F control \u003d x, for the third - F control = 2x.
The coefficient k is called rigidity springs. The stiffer the spring, the harder it is to stretch, and the greater the value of k. And the more k, the greater will be the elastic force (F control) with equal elongations (x) of different springs.
The stiffness depends on the material from which the spring is made, its shape and size.
The unit of stiffness is N/m (newton per meter). Rigidity shows how many newtons (how many forces) must be applied to a spring in order to stretch it 1 m. Or how many meters a spring will stretch if a force of 1 N is applied to stretch it. For example, a force of 1 N was applied to a spring, and it stretched by 1 cm (0.01 m). This means that its rigidity is 1 N / 0.01 m = 100 N / m.
Also, if you pay attention to the units of measurement, it becomes clear why the stiffness is measured in N / m. The elastic force, like any force, is measured in newtons, and the distance is measured in meters. In order to level the left and right sides of the equation F control = kx in units of measurement, it is necessary to reduce the meters on the right side (that is, divide by them) and add newtons (that is, multiply by them).
The relationship between the elastic force and the deformation of an elastic body, described by the formula F control \u003d kx, was discovered by the English scientist Robert Hooke in 1660, so this ratio bears his name and is called Hooke's law.
Elastic deformation is such when, after the termination of the action of forces, the body returns to its original state. There are bodies that almost cannot be subjected to elastic deformation, while for others it can be quite large. For example, placing a heavy object on a piece of soft clay will change its shape, and this piece will not return to its original state by itself. However, if you stretch the rubber band, then after you release it, it will return to its original size. It should be remembered that Hooke's law is applicable only for elastic deformations.
The formula F control \u003d kx makes it possible to calculate the third from the known two quantities. So, knowing the applied force and elongation, you can find out the rigidity of the body. Knowing the stiffness and elongation, find the elastic force. And knowing the elastic force and stiffness, calculate the change in length.
Hooke's law was discovered in the 17th century by the Englishman Robert Hooke. This discovery about the stretching of a spring is one of the laws of the theory of elasticity and plays an important role in science and technology.
Definition and formula of Hooke's law
The formulation of this law is as follows: the elastic force that appears at the moment of deformation of the body is proportional to the elongation of the body and is directed opposite to the movement of the particles of this body relative to other particles during deformation.
The mathematical notation of the law looks like this:
Rice. 1. Hooke's law formula
where Fupr- respectively, the elastic force, x is the elongation of the body (the distance by which the original length of the body changes), and k- coefficient of proportionality, called the stiffness of the body. Force is measured in Newtons, while body length is measured in meters.
To reveal the physical meaning of rigidity, it is necessary to substitute the unit in which the elongation is measured - 1 m into the formula for Hooke's law, having previously obtained an expression for k.
Rice. 2. Body stiffness formula
This formula shows that the stiffness of a body is numerically equal to the elastic force that occurs in the body (spring) when it is deformed by 1 m. It is known that the stiffness of a spring depends on its shape, size and material from which this body is made.
Elastic force
Now that we know which formula expresses Hooke's law, it is necessary to understand its basic value. The main quantity is the elastic force. It appears at a certain moment when the body begins to deform, for example, when a spring is compressed or stretched. It is directed in the opposite direction from gravity. When the force of elasticity and the force of gravity acting on the body become equal, the support and the body stop.
Deformation is an irreversible change that occurs with the size of the body and its shape. They are associated with the movement of particles relative to each other. If a person sits in an easy chair, then deformation will occur with the chair, that is, its characteristics will change. It can be of different types: bending, stretching, compression, shear, torsion.
Since the force of elasticity belongs in its origin to electromagnetic forces, you should know that it arises due to the fact that molecules and atoms, the smallest particles that make up all bodies, attract each other and repel each other. If the distance between the particles is very small, then they are affected by the repulsive force. If this distance is increased, then the force of attraction will act on them. Thus, the difference between the forces of attraction and repulsion is manifested in the forces of elasticity.
The elastic force includes the reaction force of the support and the weight of the body. The strength of the reaction is of particular interest. This is the force that acts on a body when it is placed on a surface. If the body is suspended, then the force acting on it is called the tension force of the thread.
Features of elastic forces
As we have already found out, the elastic force arises during deformation, and it is aimed at restoring the original shapes and sizes strictly perpendicular to the deformable surface. The elastic forces also have a number of features.
- they occur during deformation;
- they appear at two deformable bodies simultaneously;
- they are perpendicular to the surface with respect to which the body is deformed.
- they are opposite in direction to the displacement of body particles.
Application of the law in practice
Hooke's law is applied both in technical and high-tech devices, and in nature itself. For example, elastic forces are found in watch mechanisms, in shock absorbers in vehicles, in ropes, elastic bands, and even in human bones. The principle of Hooke's law is the basis of a dynamometer - a device with which force is measured.
You and I know that if a force acts on a body, then the body will move under the influence of this force. For example, a snowflake falls to the ground because it is pulled by the Earth. And the gravity of the Earth acts constantly, but the snowflake, having reached the roof, does not continue to fall, but stops, keeping our house dry.
From the point of view of cleanliness and order in the house, everything is correct and logical, but from the point of view of physics, there must be an explanation for everything. And if a snowflake suddenly stops moving, then a force must have appeared that counteracts its movement. This force acts in the direction opposite to the attraction of the Earth, and is equal to it in magnitude. In physics, this force, which opposes the force of gravity, is called the elastic force and is studied in the course of the seventh grade. Let's figure out what it is.
What is elastic force?
For an example explaining what an elastic force is, let's remember or imagine a simple clothesline on which we hang wet laundry. When we hang any wet thing, the rope, previously stretched horizontally, bends under the weight of the laundry and stretches slightly. Our thing, for example, a wet towel, first moves to the ground along with the rope, then stops. And so it happens when adding to the rope of each new thing. That is, it is obvious that with an increase in the force of influence on the rope, it is deformed until the moment when the forces of counteraction to this deformation become equal to the weight of all things. And then the downward movement stops. In simple terms, the work of the elastic force is to maintain the integrity of objects that we act on by other objects. And if the force of elasticity does not cope, then the body is deformed irrevocably. The rope breaks, the roof collapses under too much weight of snow, and so on. When does the force of elasticity arise? At the moment of the beginning of the impact on the body. When we hang up the laundry. And disappears when we take off our underwear. That is, when the impact stops. The point of application of the elastic force is the point at which the impact occurs. If we are trying to break the stick on the knee, then the point of application of the elastic force will be the point at which we press on the stick with the knee. This is quite understandable.
How to find the elastic force: Hooke's law
To learn how to find the elastic force, we must get acquainted with Hooke's law. The English physicist Robert Hooke was the first to establish the dependence of the magnitude of the elastic force on the deformation of the body. This dependence is directly proportional. The more deformation occurs, the greater the elastic force. I.e the formula for the elastic force is as follows:
F_control=k*∆l,
where ∆l is the amount of deformation,
and k is the stiffness factor.
The stiffness coefficient, of course, is different for different bodies and substances. To find it, there are special tables. Elastic force is measured in N/m(newtons per meter).
The force of elasticity in nature
The force of elasticity in nature- this is a flock of sparrows on a tree branch, bunches of berries on bushes or snow caps on spruce paws. At the same time, bending, but not giving up branches heroically and completely free of charge demonstrate to us the strength of elasticity.
When an external force acts on a body, it deforms (there is a change in the size, volume and often the shape of the body). In the course of deformation of a solid body, displacements of particles appear at the nodes of the crystal lattice from the initial equilibrium positions to new positions. Such a shift is prevented by the forces with which the particles interact. As a result, internal elastic forces appear, balancing external forces. These forces are applied to the deformed body. The magnitude of the elastic forces is proportional to the deformation of the body.
Definition and formula of elastic force
Definition
The force of elasticity called a force that has an electromagnetic nature, which arises as a result of deformation of the body, as a response to an external influence.
An elastic deformation is a deformation in which, after the termination of the action of an external force, the body restores its former shape and dimensions, the deformation disappears. The deformation is elastic only if the external force does not exceed a certain value, called the elastic limit. The elastic force under elastic deformations is potential. The direction of the elastic force vector is opposite to the direction of the displacement vector during deformation. Or, in another way, we can say that the elastic force is directed against the movement of particles during deformation.
Characteristics of elastic properties of solids
The elastic properties of solids are characterized by stress, which is often denoted by the letter. Stress is a physical quantity equal to the elastic force that falls on a unit section of the body:
where dF upr is the element of the body elasticity force; dS is an element of the sectional area of the body. The voltage is called normal if the vector is perpendicular to dS.
The formula for calculating the elastic force is the expression:
where - relative deformation, - absolute deformation, x - the initial value of the quantity that characterized the shape or size of the body; K is the modulus of elasticity ( at ). The reciprocal of the modulus of elasticity is called the coefficient of elasticity. Simply put, the elastic force is proportional in magnitude to the magnitude of the deformation.
Longitudinal tension (compression)
Longitudinal (unilateral) stretching consists in the fact that under the action of a tensile (compressive) force, an increase (decrease) in the length of the body occurs. The condition for the termination of this kind of deformation is the fulfillment of the equality:
where F is the external force applied to the body, Fupr is the force of elasticity of the body. The measure of deformation in the process under consideration is relative elongation (compression).
Then the modulus of the elastic force can be defined as:
where E is Young's modulus, which in the case under consideration is equal to the elastic modulus (E=K) and characterizes the elastic properties of the body; l is the initial length of the body; – length change under load F=F_upr. At 
is the cross-sectional area of the sample.
Expression (4) is called Hooke's law.
In the simplest case, consider the elastic force that occurs when the spring is stretched (compressed). Then Hooke's law is written as:
where F x is the modulus of the projection of the elastic force; k is the spring constant, x is the elongation of the spring.
Shear deformation
A shear is a deformation in which all layers of the body that are parallel to a certain plane are displaced relative to each other. When shearing, the volume of the body that has been deformed does not change. The segment on which one plane is displaced relative to the other is called an absolute shift (Fig. 1 segment AA '). If the shift angle () is small, then 
. This corner? (relative shear) characterize the relative deformation. In this case, the voltage is:
where G is the shear modulus.
Elastic Force Units
The basic unit of measurement of elastic forces (as well as any other force) in the SI system is: \u003d H
In SGS: =dyn
Examples of problem solving
Example
Exercise. What is the work of the elastic force when the spring is deformed, the stiffness, which is equal to k? If the initial extension of the spring was x 1 , the subsequent extension was x 2 .
Decision. In accordance with Hooke's law, we find the modulus of the elastic force as:
In this case, the elastic force at the first deformation will be equal to:
In the case of the second deformation, we have:
The work (A) of the elastic forces can be found as:
where is the average value of the elastic force, equal to:
S-displacement module, equal to:
The angle between the displacement vectors and the vector of elastic forces (these vectors are directed in opposite directions). We substitute expressions (1.2), (1.3), (1.5) and (1.6) into the formula for work (1.4), we get.
